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in memory of

Prof. Alexander Zabrodsky

**
Prof. Andrey Todorov (UC Santa Cruz)**

will deliver three lectures on:

**
Discriminants and Regularized Determinants on the
Moduli Space of CY Manifolds**

Lecture notesRegularized determinants and some applications

Lectures given at Hebrew University, November 19, 22, 24, 2007Bass, Jamey ; Todorov, Andrey

The analogue of the Dedekind eta function for CY manifolds. I.

J. Reine Angew. Math.599 (2006), 61--96.

(the basis of the last lecture)

Abstracts

Lecture 1.Monday , November 19th, 2007

In Room 110, Mathematics Building, at 16:00- First I will define the regularized determinant for the circle, which is the simplest CY manifold. One can show that any metric on the circle is equivalent under the action of Diff+(S) to the round metric. Thus the only invariant of the metric is the length of the circle. Then we will compute the zeta function of the Laplacian and show how it is related to Riemann zeta function. We will compute the regularized determinant.

Lecture 2.Thursday, November 22nd, 2007

In Lecture Hall 2, Mathematics Building, at 16:00- We will talk about Laplacians of flat metrics on elliptic curves. I will formulate the second Kronecker Theorem. I will point out the relation between the algebraic discriminant and the zero set of the regularized determinant, by interpreting it as the L^2 norm of some section of the natural line bundle over the moduli of elliptic curves.

Lecture 3.Sunday, November 25th, 2007

In Room 110, Mathematics Building , at 16:00- We will show how to generalize the results about the regularized determinant to K3 surfaces with some restrictions and CY manifolds with the algebraic discriminant introduced by Gelfand, Kapranov and Zelevinsky.

Alexander Zabrodsky / The Mathematics Genealogy Project

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